When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?
A. 1
B. 3
C. 5
D. 8
E. Cannot be determined
The OA is B.
I get the solution to this PS question as follow,
When x is divided by 20 the remainder is 8.
Therefore x is of form 20k + 8, where k is an integer.
When x is divided by 5, the component 5(4k + 1) is divided by 5. Hence, remainder when x is divided by 5 = remainder(3/5) = 3. Option B.
Experts, any suggestion? Thanks in advance.
When positive integer x is divided by 20, the remainder is 8
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There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"LUANDATO wrote:When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?
A. 1
B. 3
C. 5
D. 8
E. Cannot be determined
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
In this case, we aren't told how many times 20 divides into x, but this isn't a problem.
Let's just say that 20 divides into x k times.
In other words, x divided by 20 equals k with remainder 8
Applying the above rule, we can then say: x = 20k + 8 for some positive integer k
What is the remainder when x is divided by 5?
We know that: x = 20k + 8
Rewrite as: x = 20k + 5 + 3
And the factor to get: x = 5(4k + 1) + 3
So, we can see that x is 3 greater than some multiple of 5
This tells us that, if we divide x by 5, the remainder will be 3
Answer: B
Cheers,
Brent
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Note that in these types of questions, x can always equal the remainder. (8/20 is the same thing as 0 + 8/20.) You can see this if you take Brent's equation and plug 0 into the Q.LUANDATO wrote:When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?
A. 1
B. 3
C. 5
D. 8
E. Cannot be determined
The OA is B.
I get the solution to this PS question as follow,
When x is divided by 20 the remainder is 8.
Therefore x is of form 20k + 8, where k is an integer.
When x is divided by 5, the component 5(4k + 1) is divided by 5. Hence, remainder when x is divided by 5 = remainder(3/5) = 3. Option B.
Experts, any suggestion? Thanks in advance.
If x = 8, then 8/5 = 1 + 3/5, giving us a remainder of 3. The answer is B
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Hi LUANDATO,
DavidG brings up a good point  when TESTing VALUES in these types of questions, the easiest value for X is almost always the remainder itself. That having been said, you don't have to use that value to get the correct answer. If we use X = 28, then 28/20 = 1 r 8.... and the answer to the question is 28/5 = 5 r 3 > so the answer is still 3.
Final Answer: B
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DavidG brings up a good point  when TESTing VALUES in these types of questions, the easiest value for X is almost always the remainder itself. That having been said, you don't have to use that value to get the correct answer. If we use X = 28, then 28/20 = 1 r 8.... and the answer to the question is 28/5 = 5 r 3 > so the answer is still 3.
Final Answer: B
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We can create the equation:LUANDATO wrote:When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?
A. 1
B. 3
C. 5
D. 8
E. Cannot be determined
x/20 = Q + 8/20
x = 20Q + 8
When 20Q + 8 is divided by 5 we have:
(20Q + 8)/5 = 4Q + 8/5
Since 8/5 = 1 3/5, the remainder is 3.
Alternate Solution:
Since we have a remainder of 8 when x is divided by 20, x could equal 28. When we divide 28 by 5, the quotient is 5 with a remainder of 3.
Answer: B
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$$\frac{x}{20}=Q+\frac{8}{20}$$
$$x=20Q+8$$
$$when\ x\ is\ divided\ by\ 5\ i.e\ \frac{x}{5}=???$$
$$substituting\ 20Q+8=x$$
$$we\ have,\ \frac{\left(20Q+8\right)}{5}=4Q+\frac{8}{5}$$
$$=4Q+1\frac{3}{5}$$
$$Hence,\ the\ remainder\ is\ 3.\ Option\ B$$
$$x=20Q+8$$
$$when\ x\ is\ divided\ by\ 5\ i.e\ \frac{x}{5}=???$$
$$substituting\ 20Q+8=x$$
$$we\ have,\ \frac{\left(20Q+8\right)}{5}=4Q+\frac{8}{5}$$
$$=4Q+1\frac{3}{5}$$
$$Hence,\ the\ remainder\ is\ 3.\ Option\ B$$